Question

Bài 1: Thực hiện phép tính bằng cách hợp lý (nếu có thể):

1/ 3/4 + 5/4 . 2\(\dfrac{2}{3}\) - (-1/2)² : 6/5

2/ 7\(\dfrac{23}{27}\) + 11/25 + 3,25 - 23/27 + 14/25

3/ (1/9)²⁰⁰⁵ . 9²⁰⁰⁵ - 96² : 24²

4/ 2.(-3/2)² - 7/2

5/ 7.5 : (-5/3) + 2\(\dfrac{1}{2}\) : (-5/3)

6/ (3/5 + 1/2)²

7/ 0,5.(-3\(\dfrac{1}{2}\))

8/ (3\(\dfrac{4}{5}\) + 0,2)(3/14 : 6/7 -2/7)

9/ 10.(-1/2)³ + 1/4

10/ 16\(\dfrac{2}{7}\) : (-3/5) - 28\(\dfrac{2}{7}\) : (-3/5)

11/ (3\(\dfrac{1}{3}\) .1,9 +19,5 : 4\(\dfrac{1}{3}\) )(62/75 - 4/25)

Answer 1

1: \(=\dfrac{3}{4}+\dfrac{5}{4}\cdot\dfrac{8}{3}-\dfrac{1}{4}\cdot\dfrac{5}{6}=\dfrac{3}{4}+\dfrac{10}{3}-\dfrac{5}{24}\)

\(=\dfrac{18}{24}+\dfrac{80}{24}-\dfrac{5}{24}=\dfrac{93}{24}=\dfrac{31}{8}\)

2: \(=\left(7+\dfrac{23}{27}-\dfrac{23}{27}\right)+\left(\dfrac{11}{25}+\dfrac{14}{25}\right)+3.25\)

\(=7+1+3.25=8+3.25=11.25\)

3: \(=\left(\dfrac{1}{9}\cdot9\right)^{2005}-4^2=1-16=-15\)

4: \(=2\cdot\dfrac{9}{4}-\dfrac{7}{2}=\dfrac{9}{2}-\dfrac{7}{2}=1\)

5: \(=\dfrac{15}{2}\cdot\dfrac{-3}{5}+\dfrac{5}{2}\cdot\dfrac{-3}{5}=\dfrac{-3}{5}\cdot\left(\dfrac{15}{2}+\dfrac{5}{2}\right)=\dfrac{-3}{5}\cdot10=-6\)

6: \(=\left(\dfrac{6}{10}+\dfrac{5}{10}\right)^2=\left(\dfrac{11}{10}\right)^2=\dfrac{121}{100}\)

7: \(=\dfrac{1}{2}\cdot\dfrac{-7}{2}=\dfrac{-7}{4}\)